Sulfides have been widely acknowledged as one of the most promising solid electrolytes (SEs) for all-solid-state batteries (ASSBs) due to their superior ionic conductivity and favourable mechanical properties. However, the extremely poor air stability of sulfide SEs leads to destroyed structure/performance and release of toxic H2S gas, which greatly limits mass-production/practical application of sulfide SEs and ASSBs. This review is designed to serve as an all-inclusive handbook for studying this critical issue. First, the research history and milestone breakthroughs of this field are reviewed, and this is followed by an in-depth elaboration of the theoretical paradigms that have been developed thus far, including the random network theory of glasses, hard and soft acids and bases (HSAB) theory, thermodynamic analysis and kinetics of interfacial reactions. Moreover, the characterization of air stability is reviewed from the perspectives of H₂S generation, morphology evolution, mass change, component/structure variations and electrochemical performance. Furthermore, effective strategies for improving the air stabilities of sulfide SEs are highlighted, including H2S absorbents, elemental substitution, design of new materials, surface engineering and sulfide-polymer composite electrolytes. Finally, future research directions are proposed for benign development of air stability for sulfide SEs and ASSBs.